Assignment
SUNY-Stony Brook. Economics Department Economics 303: Spring 2018
Professor Meta Brown
We recommend that you complete this problem set in groups. You may hand in one problem set for up to four students. Each student's name must appear on the shared problem set.
Show your work in your answers in order to receive full credit.
1. (a) Give some examples of possible Giffen goods (you might have to do some research on the internet or in some books.)
(b) Choose one of your examples and draw an ordinary demand curve depicting the demand for this Giffen good, labelled x1, as a function of price p1.
(c) At what level of price p1 do you think the change in demand for the Giffen good first starts to decrease as price increases? Mark this price level on your graph.
2. (a) Give some examples of inferior goods and justify your answers.
(b) Choose one of your examples and draw an Engel curve depicting the demand for this inferior good, labelled x1 , as a function of income y.
(c) At what income level y do you think the change in demand for the Giffen good first starts to decrease as income increases? Mark this income level on your graph.
3. Greg has preferences represented by a utility function U(x1,x2) = x11/3x22/3. The prices of x1 (cookies) and x2 (soda) are p1 and p2, respectively. Income is equal to y. Answer the following:
(a) What kind of utility does Greg have? Write Greg's budget constraint and an equality you can use to find Greg's optimal demand choice for cookies and soda.
(b) Derive Greg's ordinary demand function for cookies.
(c) Are cookies a normal or an inferior good for Greg? How can you tell?
4. True or false, and explain your answers.
(a) If the real interest rate is positive, then one unit of future consumption can be had by giving up less than one unit of current consumption. True or False
(b) An increase in the interest rate will necessarily result in a decrease in the present value of a given stream of income. True or False.
(c) If a consumers spends all of her income, it is impossible for all goods to be inferior goods for her. True or False.
6. Multiple choice, and explain your answers.
(a) Xiaoxo has a utility function U(c1,c2) = min{c1,c2} where c1 and c2 are her consumption in periods 1 and 2, respectively. Xiaoxi earns $180 in period 1 and she will earn $66 in period 2. Xiaoxi can borrow or lend at an interest rate of 10% (r = 0.10). There is no inflation (π = 0 ). What will Xiaoxi do?
a) Xiaoxi will save 60
b) Xiaoxi will borrow 60
c) Xiaoxi will neither borrow nor lend
d) Xiaoxi will save 54.28.
(b) If a consumer views a unit of consumption in period 1 as a perfect substitute for a unit of consumption in period 2 and if the real interest rate is positive (r > 0), the consumer will:
a) Consume only in period 1.
b) Consume only in period 2.
c) Consume equal amounts in each period.
d) Consume more in period 1 than in period 2 if income elasticity exceeds 1, else would consume more in period 2 than in period 1.
e) Equalize expenditures but not consumption in the two periods.
(c) Rohitash started to work in the year 2000; back then his weekly salary was $650. He used to consume more than $50 of those dollars in orange juice at a price of $5 a quart. Now he makes more than $1000 per week and spends around $40 in orange juice at a price of
$5 per quart.
a) For Rohitash, orange juice is a Giffen Good.
b) For Rohitash, as for anyone like him, orange juice is a normal good.
c) For Rohitash, orange juice has become an inferior good.
d) For Rohitash, orange juice is always an inferior good.
e) If orange juice is an inferior good for him it is an inferior good for everyone else.
7. Xiaoxi's utility function is still U(c1,c2) = min{c1,c2}, where the arguments are the consumption in period 1 and consumption in period 2. This time the price of consumption is $1 per unit in period 1. The nominal interest rate is 7% (r = 0.07). Xiaoxi earns $2000 in period 1 and she will earn $1,070 in period 2.
a) Write Xiaoxi's budget constraint in terms of present value, assuming no inflation ( π = 0 ).
b) How much does Xiaoxi consume in the first period and how much money does she save? (The answer might not be an integer.)
c) Suppose that Xiaoxi's money income in both periods is the same as before, the interest rate is still 7%, but there is a 2% inflation rate (π = 0.02 ). How much would a unit of consumption cost in period 2? Write down Xiaoxi's budget equation given this new information.
d) How much does Xiaoxi consume in period 1 in this case? How much does she save or borrow?
e) Is Xiaoxi a saver or a borrower? How does this increase in inflation (from 0 to 0.02) affect her, does her utility increase or decrease? Depict the change in her utility in a graph in (x1, x2 ) space.
f) Suppose instead that Xiaoxi were a borrower, and again inflation increased from 0 to 0.02. Would her utility increase or decrease? Depict the change in her utility in a graph in (x1, x2) space.